{"status": "success", "data": {"description_md": "Let $f(n)$ return the number of positive divisors of $n$ (including $1$ and $n$), where $n$ is a positive integer. The integers $f(113)$, $f(x)$, $f(y)$, $f(z)$, $f(176)$ form an arithmetic sequence, in that order, where $113 \\leq x \\leq y \\leq z \\leq 176$. What is the minimum value of $x+y+z$?", "description_html": "<p>Let <span class=\"katex--inline\">f(n)</span> return the number of positive divisors of <span class=\"katex--inline\">n</span> (including <span class=\"katex--inline\">1</span> and <span class=\"katex--inline\">n</span>), where <span class=\"katex--inline\">n</span> is a positive integer. The integers <span class=\"katex--inline\">f(113)</span>, <span class=\"katex--inline\">f(x)</span>, <span class=\"katex--inline\">f(y)</span>, <span class=\"katex--inline\">f(z)</span>, <span class=\"katex--inline\">f(176)</span> form an arithmetic sequence, in that order, where <span class=\"katex--inline\">113 \\leq x \\leq y \\leq z \\leq 176</span>. What is the minimum value of <span class=\"katex--inline\">x+y+z</span>?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Holiday Contest 2025 - Team Round - Problem 9", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}